Question

Consider the following statements
(a) The pH of a mixture containing $400\, mL$ of $0.1\, M \,H_2SO_4$ and $400\, mL$ of $0.1\, M \,NaOH$ will be approximately $1.3.$
(b) Ionic product of water is temperature dependent.
(c) A monobasic acid with $K_a = 10^{-5}$ has a $pH = 5$. The degree of dissociation of this acid is $50\%$.
(d) The Le Chatelier's principle is not applicable to common-ion effect. the correct statement are :

• A. (a), (b) and (d)
• B. (a), (b) and (c)
• C. (a) and (b)
• D. (b) and (c)

Answer 1

Answer: (B)

(a) $H_2SO_4 + 2NaOH \rightarrow Na_2SO_4 + 2H_2O$
$400 \times .1 =40 400\times .1=40$
20 $ $ 0
$\therefore \left[H^{+}\right] = \frac{20\times2}{800} =\frac{1}{20} \Rightarrow pH = - \log \left(\frac{1}{20} \right) $
$ \therefore pH = 1.3 $ so (a) is correct
(b) $\log\left(\frac{Kw_{2}}{Kw_{1}}\right) = \frac{\Delta H}{2.303R} \left[\frac{1}{T_{1}} - \frac{1}{T_{2}}\right] $
so ionic product of water is temp. dependent hence (b) is correct.
(c) $ K_{a} = 10^{-5} , pH = 5 \Rightarrow \left[H^{+}\right] = 10^{-5} $
$ K_{a} = \frac{c\alpha^{2}}{\left(1-\alpha\right) } \Rightarrow K_{a} = \frac{\left[H^{+}\right].\alpha}{\left(1-\alpha\right)} $
$ \therefore 10^{-5} = \frac{10^{-5} .\alpha}{\left(1-\alpha\right)} \Rightarrow 1 - \alpha=\alpha\Rightarrow \alpha = \frac{1}{2} =50\%$
so (c) is correct.
(d) Le-chatelier's principle is applicable to common -Ion effect so option (d) is wrong